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Introduction

In this paper we will discuss the basics of statistical analysis related to a real world problem. A law firm investigates a layoff case in QFC Company – a number of former employees has approached this firm saying that there is an age discrimination in this company. Older employees which were laid off are not hired back as quickly as younger. This statistical research will be entered as evidence on the court case in 9 months.

Body

We are given with the data of 50 observations; each observation represents employee’s characteristics. There are 7 variables used in this study.

Weeks – the number of weeks the individual was laid off

Age – the age of the individual
Tenure – for how many years person was working in QFC
Education – years of education completed
Married – whether the individual is married or not
Head – whether the individual is a head of household or not
Position – the position held by the individual
Our goal is to check whether the number of weeks the individual was laid off is associated with the age of the individual. However, there are other options to check. We are interested to analyze which variable are related to Weeks variable and if any other variables have significant impact on Weeks.

Start with recoding categorical and ordinal data in numerical data and dummy variables.

Married: 0 – NO, 1 – YES
Head: 0 – NO, 1 – YES
Position: 1 – Floor, 2 – Manager, 3 – Dept Head (Warning! In this case I assume that Dept Head is higher than Manager, I’m not sure how it is determined in your country. If I’m wrong, please contact me and I will revise shortly).
Now run descriptive statistics for each variable to understand the distribution of these variables. I describe the data my married factor, by head factor and by position factor to see if there any significant differences in Weeks between the groups.

Descriptive Statistics: Weeks

Results for Married = 0; Head = 1

Variable Position N N* Mean SE Mean StDev Minimum Q1 Median

Weeks 1 10 0 55,30 8,42 26,63 11,00 40,00 59,00
2 1 0 25,000 * * 25,000 * 25,000
3 4 0 27,50 6,66 13,33 8,00 13,50 32,50

Variable Position Q3 Maximum

Weeks 1 74,50 94,00
2 * 25,000
3 36,50 37,00
Results for Married = 1; Head = 0

Variable Position N N* Mean SE Mean StDev Minimum Q1 Median

Weeks 1 10 0 56,10 8,29 26,22 12,00 35,50 57,00
2 3 0 29,3 13,8 24,0 15,0 15,0 16,0
3 3 0 50,3 18,6 32,3 16,0 16,0 55,0

Variable Position Q3 Maximum

Weeks 1 74,75 98,00
2 57,0 57,0
3 80,0 80,0
Results for Married = 1; Head = 1
Variable Position N N* Mean SE Mean StDev Minimum Q1 Median

Weeks 1 16 0 38,81 5,36 21,45 8,00 20,00 35,50

2 1 0 20,000 * * 20,000 * 20,000
3 2 0 48,0 42,0 59,4 6,0 * 48,0

Variable Position Q3 Maximum

Weeks 1 58,00 79,00
2 * 20,000
3 * 90,0
If we look at the mean values we can see that the mean value of weeks is significantly different within groups and between groups. This means that each variable should be taken in consideration in the multiple regression model.

Create multiple regression equation taking Weeks as dependent variable and others as independent variables.

According to the ANOVA results, the model is significant (F=23.947, p<0.001). The coefficient of determination R-squared shows that approximately 76.97% of Weeks variance is explained by this model. However, if we take the most common level of significance alpha of 0.05, not all variables are significant. The p-values of Tenure, Married, Head and Position are higher than 0.05. These variables are insignificantly affect Weeks and may be excluded from the model (at 5% level of significance).
There are two factors left which have a real impact on Weeks. They are Age and Education. Looking at the signs of the coefficients of these variables it can be concluded that there is a positive association between Age and Weeks and there is a negative association between Education and Weeks.

Conclusion (Memorandum to Mr. Lemond)

A statistical research was performed to check if there is enough evidence to say that a number of former employees of QFC are right in their suspicions regarding the age discrimination in QFC Company. In this research a number of factors were taken in consideration to investigate how they affect the number of weeks the individual was laid off before taking a new job. These factors are the age of the individual, how many years person was working in QFC, years of employee’s education completed, whether the individual is married or not, whether the individual is a head of household or not and the position held by the individual in QFC (Floor, Manager or Dept Head). The results of the study support the position of the former employees group. However, there is a significant aspect which the law company should take in consideration: not only age is significantly associated with a number of weeks laid off. There is another one significant factor – a number of years of education completed. It has appeared that the fewer years individual have studied, the more time he was laid off. In other words, well educated employees have significantly less problems with finding a new job than those who are not such well educated individuals. This issue gives QFC Company an ability to defend their position during the court case – they may say that the problem is not just in age, the main issue is employees’ education level. The court may approve their point of view and in such case former employees will lose the case.

Works Cited

A. Sen, M. Srivastava, Regression Analysis — Theory, Methods, and Applications, Springer-Verlag, Berlin, 2011 (4th printing).